Degenerate elliptic systems and applications to Ginzburg-Landau type equations, part I

This paper has three topics. In Sect. 1, we present our results on the regularity and a priori estimates for solutions of p-harmonic systems with Holder continuous coefficients. Such systems come up in the study of Ginzburg-Landau type functional in higher dimensions. In Sect. 2, we study a stability inequality, which, in addition to its applications in the study of Ginzburg-Landau type functional, is of independent interest. In Sects. 3 and 4, we prove that for any sequence of minimizers of the higher dimensional Ginzburg-Landau type functional, a subsequence converges strongly away from a finite number of points, generalizing some of the two dimensional results of Bethuel, Brezis, and Hélein.